<p>This work proposes the Lie group method via a one-dimensional optimal system to construct some more exact invariant solutions of the (2+1)-dimensional KdV-mKdV equation. Using Lie symmetry, we demonstrate Lie infinitesimal generators, potential vector fields, and their commutative and adjoint relations. Additionally, Lie vectors are used to build an optimal system of the one-dimensional subalgebras. Meanwhile, the KdV-mKdV equation’s Lie symmetry reductions are derived from the optimal system. A repetitive process of Lie symmetry reductions between the considered vectors, utilizing single, double, triple, and quadruple combinations, turns the KdV-mKdV equation into non-linear ordinary differential equations with many group invariant solutions. In order to elucidate the significance of the governing equation, numerical simulation is used to trace the exact solutions. The resulting graphical structures include kink, line, single soliton, multisoliton, cusp, parabolic, lump, and stationary wave profiles. These results help numerous authors to understand the complex nature of various nonlinear phenomena throughout diverse scientific disciplines, including plasma physics, internal gravity waves, fluid mechanics, crystal lattice theory, nonlinear optics, and Bose-Einstein condensates.</p>